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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Asymptotic estimates for a two-dimensional problem with polynomial nonlinearity
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by Adimurthi and Massimo Grossi
Proc. Amer. Math. Soc. 132 (2004), 1013-1019
DOI: https://doi.org/10.1090/S0002-9939-03-07301-5
Published electronically: November 10, 2003

Abstract:

In this paper we give asymptotic estimates of the least energy solution $u_p$ of the functional \begin{equation*} J(u) =\int _\Omega |\nabla u|^2 \quad \text {constrained on the manifold }\int _\Omega |u|^{p+1}=1\end{equation*} as $p$ goes to infinity. Here $\Omega$ is a smooth bounded domain of $\mathbb {R}^2$. Among other results we give a positive answer to a question raised by Chen, Ni, and Zhou (2000) by showing that $\lim \limits _{p\rightarrow \infty }||u_{p}||_{\infty }=\sqrt e$.
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Bibliographic Information
  • Adimurthi
  • Affiliation: T.I.F.R. Centre, P.O. Box 1234, Bangalore 560012, India
  • Email: aditi@math.tifrbng.res.in
  • Massimo Grossi
  • Affiliation: Università di Roma “La Sapienza", P.le Aldo Moro, 2, 00185 Roma, Italy
  • Email: grossi@mat.uniroma1.it
  • Received by editor(s): September 7, 2002
  • Published electronically: November 10, 2003
  • Additional Notes: Supported by M.U.R.S.T., project “Variational methods and nonlinear differential equations"
  • Communicated by: David S. Tartakoff
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1013-1019
  • MSC (2000): Primary 35J20, 35B40
  • DOI: https://doi.org/10.1090/S0002-9939-03-07301-5
  • MathSciNet review: 2045416